Question

Elimination of arbitrary constants $A$ and $B$ from $y = Ae^x + Be^{-2x}$ gives the differential equation:

• A. $\frac{d^2y}{dx^2} + \frac{dy}{dx} - 2y = 0$
• B. $\frac{d^2y}{dx^2} + \frac{dy}{dx} + 2y = 0$
• C. $\frac{d^2y}{dx^2} - \frac{dy}{dx} - 2y = 0$
• D. $\frac{d^2y}{dx^2} - 2\frac{dy}{dx} + y = 0$
• E. $\frac{d^2y}{dx^2} + 2\frac{dy}{dx} + y = 0$

Hint:

Exponential solutions directly give roots of characteristic equation.

Answer 1

The Correct Option is A